Question

The 7th term of gp is 8 times the 4th term.what will be the 1st term if its 5th term is 48?

Answer 1

In the GP, the 7th term is 8 times the 4th term. So

ar^6 = 8ar^3, or

r^3 = 8 or r = 2.

ar^4 = 48, or a = 48/r^4 = 48/16 = 3.

The first term is 3.

Hope it's help you
Please mark me in the brain list answer

Answer 2

Let ,
common ratio = r = ?

first term = a = ?

5th term = T5 = 48

7th term = T7 = ar^6. (because Tn = a(r)^n-1

4th term = T4 = ar³
_______________________

T7 = 8 × T4

ar^6 = 8 × ar³

ar^6/ar³ = 8

r^6/r³ = 8

r^6-3 = 8

r³ = 8

(r)³ = (2)³

r = 2 .
____________

T5 = 48

ar⁴ = 48

a(2)⁴ = 48

a16 = 48

a = 48/16

a = 3
____________

so , common ratio = r = 2

first term = a = 3 .
_________________